1. Field of the Invention
This application relates to use of a computer system for trouble diagnosis and performance forecasting, and more particularly to techniques executed in a computer system for performance fitting, diagnosing, and forecasting of telephone connections based on curve fitting of data points involving telephone cable characteristics.
2. Description of Related Art
Numerous types of procedures involve many steps which are associated with particular components of the procedures. Each component in turn may have particular characteristics which, along with other factors, dictate the performance of each component. Having information related to component performances is advantageous for making diagnoses of trouble, minimizing costs, making repairs, and suggesting new, more efficient alternatives. Sometimes, however, knowing the performance of each component is neither easy nor even desirable, even if all the performances could be known, because this amount of information would be too unwieldy. Instead, the performances of the components of a realization may be mapped to an overall performance of the realization. The overall performance gives an indication of the global success of the procedure.
A telephone cable connection, as well as other multi-component processes, is an example where performance or trouble incidence is generally recorded for the entire connection, rather than the individual components. Common analysis of trouble involves an aggregate categorization of trouble type for each connection. However, because, in general, each connection may have a different configuration, these common approaches to trouble analysis preclude a diagnosis of its components. Thus, an intuitive and anecdotal examination of these aggregate trouble frequencies are sometimes used to subjectively assess component repair and replacement policies.
More objective approaches, such as the classical technique of using logistic regression to model cable trouble rates, do exist. However, although superficially relating holistic cable trouble and aggregate segment characteristics, these approaches do not account for the probabilistic structure relating cable trouble to component trouble, and do not allow an appropriate mathematical form for component trouble.
These traditional aggregate techniques do not objectively inform managers of the effects of their policies and tactics for individual components. The characteristics of the components cannot be related to trouble types and rates. The logistic regression solution does not appropriately exploit the relationship in trouble probabilities among the cable components. Although these techniques might be augmented by using more sophisticated nonlinear regression analysis, the high data storage and computational power requirements may be prohibitive.
According to the present invention, statistical relationships between aggregate troubles and process (e.g., cable) components are constructed in a manner that facilitates the fitting of the overall performance to field data with a relatively small number of free parameters. Such fitting can aid in the diagnosing and forecasting of performance problems that can be used to make policy decisions pertaining to what apparatus and technology to use. These decisions may then be evaluated by proper benchmarking of the apparatus. The present method has sufficiently low data storage and computational demands to permit its implementation on virtually any microcomputer.
These desirable attributes of the present method are achieved by a judicious choice of a trial function, which relates component characteristics and component performances, to be used for data fitting. A good choice for such a function would lead to a number of useful functions of the characteristics instead of all the characteristics themselves. Because the number of such functions of the characteristics is considerably less than the total number of characteristics across a connection, a reduction in the data required to perform the curve fitting may be possible.
Specifically, a method executed in a computer system for diagnosing, and predicting trouble causes in a process involving realizations of performance is presented. The ith realization has ni steps and the performance is a function of a c-component vector of characteristics, the performance and vector having a value of xcex8i[j, xi(j)] and xi(j), respectively, at the jth step of the ith realization. (The component of a vector should not be confused with the component of a connection; the former refers to each of the numbers in an ordered set defining a column or row vector, the latter is associated with each of the ni steps of connection i.) The method comprises a) expressing an overall performance, "psgr"i, as a function, xcfx86i, of the performance at each of the ni steps, "psgr"i=xcfx86i{xcex8i[1, xi(1)], xcex8i[2, xi(2)], . . . , xcex8i[ni, xi(ni)]}; b) choosing a function, f, of a d-component vector of parameters, xcex2, and the c-component vector of characteristics with which to approximate the performances, xcex8i[j, xi(j)]≈f[xcex2, xi(j)]. The function f is chosen such that the overall performance, "psgr"i, can be written as a function, xcex3i, of the d-component vector of parameters and r c-component vectors, si,1, si,2, . . . , and si,r, that depend on the ni characteristic vectors xi(1), xi(2), . . . , and xi(ni),                               ψ          i                =                  xe2x80x83                ⁢                              φ            i                    ⁢                      {                                          f                ⁡                                  [                                      β                    ,                                                                  x                        i                                            ⁡                                              (                        1                        )                                                                              ]                                            ,                              f                ⁡                                  [                                      β                    ,                                                                  x                        i                                            ⁡                                              (                        2                        )                                                                              ]                                            ,              …              ⁢                              xe2x80x83                            ,                              f                ⁡                                  [                                      β                    ,                                                                  x                        i                                            ⁡                                              (                                                  n                          i                                                )                                                                              ]                                                      }                                                  ≡                  xe2x80x83                ⁢                              γ            i                    ⁢                      {                          β              ,                                                s                                      i                    ,                    1                                                  ⁡                                  [                                                                                    x                        i                                            ⁡                                              (                        1                        )                                                              ,                                                                  x                        i                                            ⁡                                              (                        2                        )                                                              ,                    …                    ⁢                                          xe2x80x83                                        ,                                                                  x                        i                                            ⁡                                              (                                                  n                          i                                                )                                                                              ]                                            ,                                                                        xe2x80x83                ⁢                                            s                              i                ,                2                                      ⁡                          [                                                                    x                    i                                    ⁡                                      (                    1                    )                                                  ,                                                      x                    i                                    ⁡                                      (                    2                    )                                                  ,                …                ⁢                                  xe2x80x83                                ,                                                      x                    i                                    ⁡                                      (                                          n                      i                                        )                                                              ]                                ,          …          ⁢                      xe2x80x83                    ,                                                  xe2x80x83                ⁢                                            s                              i                ,                r                                      ⁡                          [                                                                    x                    i                                    ⁡                                      (                    1                    )                                                  ,                                                      x                    i                                    ⁡                                      (                    2                    )                                                  ,                …                ⁢                                  xe2x80x83                                ,                                                      x                    i                                    ⁡                                      (                                          n                      i                                        )                                                              ]                                }                    
where r less than ni; c) finding a best vector of parameters that results in a best fit of the function xcex3i(xcex2, si,1, si,2, . . . , si,r) to data points corresponding to the overall performance as a function of the r c-component vectors, si,1, si,2, . . . , and si,r.
In a specific embodiment, the method further comprises predicting the overall performance of a realization from r c-component vectors that correspond to si,1, si,2, . . . , and si,r by utilizing the best vector of parameters.
In another embodiment, the step of choosing a function, f, of a d-component vector of parameters, xcex2, and the c-component vector of characteristics, includes choosing a function, f, of a c-component vector of parameters, xcex2, and the c-component vector of characteristics.
In a specific embodiment, the method includes expressing the overall performance, "psgr"i, as "psgr"i=xcex8i[1, xi(1)]xcex8i[2, xi(2)] . . . xcex8i[ni, xi(ni)], and choosing the function f=exp[xcex2xc2x7xi(j)], where xcex2xc2x7xi(j) denotes an inner product of xcex2 and xi(j).
In an embodiment of the invention, fitting the function xcex3i(xcex2, si,1, si,2, . . . , si,r) proceeds by utilizing a microprocessor, and a regression algorithm, which may employ the Levenberg-Marquardt method, to estimate the vector of parameters, xcex2, that approximately maximizes agreement between the function xcex3i(xcex2, si,1, si,2, . . . si,r) and the data points. The Levenberg-Marquardt method may utilize a figure-of-merit function that measures this agreement.
In an other embodiment of the present invention, a method executed in a computer system for predicting trouble in a telephone connection is presented comprising a) characterizing a jth component of a sequence of ni components of an ith telephone connection by a c-component vector of characteristics xi(j); b) assigning a performance xcex8i[j,xi(j)] to the jth component of the ith telephone connection; c) approximating the performance as xcex8i[j, xi(j)]=exp[xcex2xc2x7xi(j)], where xcex2 is a c-component vector of parameters and xcex2xc2x7xi(j) denotes an inner product of xcex2 and xi(j); d) defining an overall performance of the ith telephone connection as the product of the performances over the components of the ith realization,             ψ      i        =                  ∏                  j          =          1                ni            ⁢                        θ          i                ⁡                  [                      j            ,                                          x                i                            ⁢                              (                j                )                                              ]                      ;
e) varying the vector of parameters xcex2 to find a best vector of parameters that fits a curve                               ψ          i                =                  exp          ⁡                      [                          β              ·                                                ∑                                      j                    =                    1                                    ni                                ⁢                                                      x                    i                                    ⁡                                      (                    j                    )                                                                        ]                                                            =                      exp            ⁡                          (                              β                ·                                  s                  i                                            )                                      ,            
where si=xi(1)+xi(2)+ . . . +xi(ni), through data points corresponding to the overall performance versus si.
In another embodiment, this last method further comprises predicting the overall performance of a realization from a c-component vector, that corresponds to si, by utilizing the best vector of parameters.
Also presented is a system for diagnosing, and predicting trouble causes in a process involving realizations of performance. The ith realization has ni steps and the performance is a function of a c-component vector of characteristics. The performance and c-component vector have a value of xcex8i[j, xi(j)] and xi(j), respectively, at the jth step of the ith realization, comprising a) a computer; b) instructions for the computer to express an overall performance, "psgr"i, as a function, xcfx86i, of the performance at each of the ni steps, "psgr"i=xcfx86i{xcex8i[1, xi(1)], xcex8i[2, xi(2)], . . . xcex8i[ni, xi(ni)]}; c) instructions for the computer to choose a function, f, of a d-component vector of parameters, xcex2, and the c-component vector of characteristics with which to approximate the performances, xcex8i[j, xi(j)]≈f[xcex2, xi(j)], such that the overall performance, "psgr"i, can be written as a function, xcex3i, of the d-component vector of parameters and r c-component vectors, si,1, si,2, . . . , and si,r, that depend on the ni characteristic vectors xi(1), xi(2), . . . , and xi(ni),                               ψ          i                =                  xe2x80x83                ⁢                              φ            i                    ⁢                      {                                          f                ⁡                                  [                                      β                    ,                                                                  x                        i                                            ⁡                                              (                        1                        )                                                                              ]                                            ,                              f                ⁡                                  [                                      β                    ,                                                                  x                        i                                            ⁡                                              (                        2                        )                                                                              ]                                            ,              …              ⁢                              xe2x80x83                            ,                              f                ⁡                                  [                                      β                    ,                                                                  x                        i                                            ⁡                                              (                                                  n                          i                                                )                                                                              ]                                                      }                                                  ≡                  xe2x80x83                ⁢                              γ            i                    ⁢                      {                          β              ,                                                s                                      i                    ,                    1                                                  ⁡                                  [                                                                                    x                        i                                            ⁡                                              (                        1                        )                                                              ,                                                                  x                        i                                            ⁡                                              (                        2                        )                                                              ,                    …                    ⁢                                          xe2x80x83                                        ,                                                                  x                        i                                            ⁡                                              (                                                  n                          i                                                )                                                                              ]                                            ,                                                                        xe2x80x83                ⁢                                            s                              i                ,                2                                      ⁡                          [                                                                    x                    i                                    ⁡                                      (                    1                    )                                                  ,                                                      x                    i                                    ⁡                                      (                    2                    )                                                  ,                …                ⁢                                  xe2x80x83                                ,                                                      x                    i                                    ⁡                                      (                                          n                      i                                        )                                                              ]                                ,          …          ⁢                      xe2x80x83                    ,                                                  xe2x80x83                ⁢                                            s                              i                ,                r                                      ⁡                          [                                                                    x                    i                                    ⁡                                      (                    1                    )                                                  ,                                                      x                    i                                    ⁡                                      (                    2                    )                                                  ,                …                ⁢                                  xe2x80x83                                ,                                                      x                    i                                    ⁡                                      (                                          n                      i                                        )                                                              ]                                }                    
where r less than ni; and d) instructions for the computer to find a best vector of parameters that results in a best fit of the function xcex3i(xcex2, si,1, si,2, . . . , si,r) to data points corresponding to the overall performance as a function of the r c-component vectors, si,1, si,2, . . . , and si,r.
In another embodiment, in the previous system for diagnosing, and predicting trouble causes, an overall performance of a process with given characteristics is forecast by using the function xcex3i(xcex2, si,1, si,2, . . . , si,r) with the best vector of parameters.
In yet another embodiment, a system is presented for predicting trouble in a telephone connection. A jth component of a sequence of ni components of an ith telephone connection is characterized by a c-component vector of characteristics xi(j). The system comprises a) a computer; b) instructions to the computer to assign a performance xcex8i[j, xi(j)], that depends on the vector of characteristics, to the jth component of the ith telephone connection; c) instructions to the computer to (i) approximate the performance as xcex8i[j, xi(j)]=exp[xcex2xc2x7xi(j)], where xcex2 is a c-component vector of parameters and xcex2xc2x7xi(j) denotes an inner product of xcex2 and xi(j), and (ii) define an overall performance of the ith telephone connection as the product of the performances over the components of the ith realization,             ψ      i        =                  ∏                  j          =          1                ni            ⁢                        θ          i                ⁡                  [                      j            ,                                          x                i                            ⁢                              (                j                )                                              ]                      ;      xe2x80x83    ⁢  and
e) means for varying the vector of parameters xcex2 to find a best vector of parameters to fit a curve                               ψ          i                =                  exp          ⁡                      [                          β              ·                                                ∑                                      j                    =                    1                                    ni                                ⁢                                                      x                    i                                    ⁡                                      (                    j                    )                                                                        ]                                                            =                      exp            ⁡                          (                              β                ·                                  s                  i                                            )                                      ,            
where si=xi(1)+xi(2)+ . . . +xi(ni), to data points corresponding to the overall performance versus si.
In another embodiment, a system to diagnose trouble causes in telephone cable segments when trouble data are available only for entire cables is presented. The system includes a computer; means for approximating an overall performance of a telephone connection depending on n c-component vectors of characteristics so that the overall performance can be modeled by using a function with adjustable c-component vectors of parameters, the vectors of parameters being less in number than n; and means for varying the adjustable c-component vectors of parameters to find best-fit vectors of parameters to fit a curve to data points. The means for varying the adjustable c-component vectors of parameters can include using a regression algorithm. The diagnosis proceeds by examining and interpreting the vector of parameters xcex2.